cp's OEIS Frontend

A318809 Number of necklace permutations of the multiset of prime indices of n > 1.

%I A318809 #5 Sep 05 2018 06:16:24
%S A318809 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,
%T A318809 1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,2,1,1,
%U A318809 1,2,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1
%N A318809 Number of necklace permutations of the multiset of prime indices of n > 1.
%C A318809 A necklace is a finite sequence that is minimal among its cyclic permutations.
%C A318809 a(1) = 1 by convention.
%e A318809 The a(144) = 3 necklace permutations of {1,1,1,1,2,2} are: (111122), (111212), (112112).
%t A318809 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A318809 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A318809 Table[Length[Select[Permutations[primeMS[n]],neckQ]],{n,2,200}]
%Y A318809 Cf. A000670, A000740, A008480, A008965, A056239, A059966, A112798, A298941, A318810.
%K A318809 nonn
%O A318809 1,30
%A A318809 _Gus Wiseman_, Sep 04 2018